they’ll teach you, correctly, that if the government
  spends n dollars to stimulate the economy, it doesn’t
  really matter what it’s spent on

Forgive my ignorance on these matters - I know that if the government pays a work crew the work crew ends up with money in their pockets regardless of what specifically they build; but surely if you pay a work crew to build a useful freeway or a bridge (or a rail system if you prefer) you also get the economic benefits of that freeway, bridge or railway; whereas if you pay the same work crew to dig a useless hole you don't get those economic benefits?